A dual-band filtering antenna based on a double-layer structure working in the n77/n78/n79 frequency bands is proposed. The antenna consists of two rectangular radiation patches on the upper substrate, step impedance resonators and two L-shaped branches on the lower substrate. The two dielectric substrates(FR4) are connected by probes. The two rectangular radiation patches on the upper dielectric substrate excite two resonant modes, among which the high-band resonance is employed to form the n79 frequency band, and the low-frequency resonance is employed to form the n77/n78 frequency band. In order to obtain the double bandpass filtering effect, a Step Impedance Resonator(SIR) is introduced into the lower dielectric substrate to form an out-of-band radiation nulls between the two frequency bands. In addition, the L-shaped branches on the lower substrate can introduce additional resonance points to expand the bandwidth of the antenna. The structure is optimized by High Frequency Simulation Software(HFSS). Its simulation results and test results cover the two frequency bands of 3.37~3.53 GHz(n77/n78) and 4.55~4.64 GHz(n79). The proposed antenna can be used for sub-6 GHz 5G wireless communication applications.